The specularity and the reflections are tied together. If there is no specularity, there is no reflection. The brighter the spec, the more visible the reflection is. Your reflection is only as strong as your specularity. If your specularity is at 50 and your reflection is at a 100, your reflection is at 50.
Your specularity highlights should remain with whatever reflection you put on. Here is an example of an object with varied specularities and reflections:
https://www.dropbox.com/s/4awa6utijq...pecularity.jpg
If you need more shine, you can always ad rim lighting or rim radial to your object. If you don't know how, here's a quick how to
https://www.dropbox.com/s/ara65fxcnb...mRadialHow.jpg
I hope this clears up the questions you have.